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Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0002-5604-493X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0002-5328-9560
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0001-9635-0301
Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-3860-761X
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2014 (English)In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2014, p. 683-690Conference paper, Published paper (Refereed)
Abstract [en]

To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD)method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations,is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTDscheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source ofelectromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of AbsorbingBoundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC)surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTDscheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of thecomputer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can berather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTDalgorithm.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014. p. 683-690
Keyword [en]
Electromagnetic scattering, Maxwell’s equations, Finite Difference Time-Domain (FDTD) method, Courant stability condition, Absorbing boundary condition, point-wise convergence, semi-norm
National Category
Mathematics Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-26059DOI: 10.1063/1.4904639ISI: 000347812200082Scopus ID: 2-s2.0-85031866488ISBN: 978-0-7354-1276-7 (print)OAI: oai:DiVA.org:mdh-26059DiVA, id: diva2:752689
Conference
ICNPAA 2014 World Congress: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik, Norway, July 15-18, 2014.
Projects
RALF3, the research project for Embedded High Performance Architecture at Mälardalen University and KK-Stiftelsen (The Swedish Knowledge Foundation)EUROWEB Project funded by the Erasmus Mundus Action II programme of the European Commission, (http://www.mrtc.mdh.se/euroweb)
Funder
Swedish Foundation for Strategic Research
Available from: 2014-10-06 Created: 2014-10-06 Last updated: 2017-11-02Bibliographically approved
In thesis
1. Mathematical Tools Applied in Computational Electromagnetics for a Biomedical Application and Antenna Analysis
Open this publication in new window or tab >>Mathematical Tools Applied in Computational Electromagnetics for a Biomedical Application and Antenna Analysis
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To ensure a high level of safety and reliability of electronic/electric systems EMC (electromagnetic compatibility) tests together with computational techniques are used. In this thesis, mathematical modeling and computational electromagnetics are applied to mainly two case studies. In the first case study, electromagnetic modeling of electric networks and antenna structures above, and buried in, the ground are studied. The ground has been modelled either as a perfectly conducting or as a dielectric surface.  The second case study is focused on mathematical modeling and algorithms to solve the direct and inverse electromagnetic scattering problem for providing a model-based illustration technique. This electromagnetic scattering formulation is applied to describe a microwave imaging system called Breast Phantom. The final goal is to simulate and detect cancerous tissues in the human female breast by this microwave technique.  

The common issue in both case studies has been the long computational time required for solving large systems of equations numerically. This problem has been dealt with using approximation methods, numerical analysis, and also parallel processing of numerical data. For the first case study in this thesis, Maxwell’s equations are solved for antenna structures and electronic networks by approximation methods and parallelized algorithms implemented in a LAN (Local Area Network). In addition, PMM (Point-Matching Method) has been used for the cases where the ground is assumed to act like a dielectric surface. For the second case study, FDTD (Finite-Difference Time Domain) method is applied for solving the electromagnetic scattering problem in two dimensions. The parallelized numerical FDTD-algorithm is implemented in both Central Processing Units (CPUs) and Graphics Processing Units (GPUs).

Abstract [sv]

För att säkerställa människors säkerhet och tillförlitligheten hos elektriska/elektroniska system används EMC (elektromagnetisk kompatibilitet)-tester i kombination med matematisk modellering. För att undersöka biologiska vävnaders egenskaper används så kallade elektromagnetiska spridningsmetoder vid sidan om elektromagnetisk modellering. I denna avhandling har matematisk modellering och beräkningsmetoder använts för huvudsakligen två fallstudier. Den första fallstudien handlar om att analysera antennstrukturer och elektriska nät ovanför, och nergrävda i marken. Marken har modellerats antingen som en elektriskt ledande yta eller en dielektrisk yta. Den andra fallstudien fokuserar på matematisk modellering och algoritmer för att lösa ett elektromagnetiskt spridningsproblem för att beskriva en modellbaserad illustrationsteknik. Spridningsformuleringen tillämpas för att modellera ett avbildningssystem som använder mikrovågor, kallat Bröstfantomen. Det slutliga målet är att upptäcka cancervävnader i kvinnobröst genom denna mikrovågsteknik.

Flaskhalsen i de båda fallstudierna har visat sig vara de långa beräkningstider som krävs för att lösa stora numeriska system. För att lösa problemet har approximationsmetoder, numerisk analys och även parallella beräkningar genomförts i detta arbete. För den första fallstudien har Maxwells ekvationer lösts genom CEM (Complex Image Methods) och med parallellisering i ett LAN (Local Area Network). I de fall där marken betraktas som en dielektrisk yta, har PMM (Point-Matching Method) tillämpats. I samband med den andra fallstudien har FDTD (Finite-Difference Time Domain) metoder tillämpats för att lösa ett elektromagnetiskt spridningsproblem i två dimensioner. En parallelliserad FDTD-algoritm har implementerats i både CPU:s (Central Processing Units) och GPU:s (Graphics Processing Units).

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2015
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 176
National Category
Mathematics Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-27764 (URN)978-91-7485-200-4 (ISBN)
Public defence
2015-05-12, Delta, Mälardalens högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Projects
RALF3
Funder
Swedish Foundation for Strategic Research
Available from: 2015-04-02 Created: 2015-03-27 Last updated: 2017-09-28Bibliographically approved

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Publisher's full textScopushttp://scitation.aip.org/content/aip/proceeding/aipcp/1637

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Monsefi, FaridCarlsson, LinusRancic, MilicaOtterskog, MagnusSilvestrov, Sergei

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